Question

If the circumferences of a circle and the perimeter of a square are equal, then the

• A. Circle and the square have equal, area
• B. Circle has larger area than the square
• C. Square has larger area than the circle
• D. Area of the square is double that of the circle

Answer 1

The correct option is B Circle has larger area than the square

Let a square have side 'a' cm and circle have radius 'r'.

Given circumference of circle = perimeter of the square

$⟹2\pi r=4aorr=\frac{2a}{\pi }$
area of circle = $\pi r^2$ and area of square = $a^2$

Area of circle in terms of side of square = $\frac{4}{\pi }{a}^2$

Comparing their areas, we can say that the area of circle > area of the square .